Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 71
... third , BE , EF are greater than BF ; but AE is equal to EB ; therefore AE and EF , that is , AF , is greater than BF : again , because BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides BE , EF are equal to ...
... third , BE , EF are greater than BF ; but AE is equal to EB ; therefore AE and EF , that is , AF , is greater than BF : again , because BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides BE , EF are equal to ...
Página 100
... third angle . Take any straight line AB , and divide ( 11. 2. ) it in the point C , so that the rectangle AB , BC may be equal to the square of AC ; and from the centre A , at the distance AB , describe the circle BDE , in which place ...
... third angle . Take any straight line AB , and divide ( 11. 2. ) it in the point C , so that the rectangle AB , BC may be equal to the square of AC ; and from the centre A , at the distance AB , describe the circle BDE , in which place ...
Página 103
... third angle to the third angle : therefore the straight line KC is equal to CL , and the angle FKC to the angle FLC and because KC is equal to CL , KL is double of KC in the same manner , it may be shown that HK is double of BK and ...
... third angle to the third angle : therefore the straight line KC is equal to CL , and the angle FKC to the angle FLC and because KC is equal to CL , KL is double of KC in the same manner , it may be shown that HK is double of BK and ...
Página 105
... third part of two right angles : In the E B same manner it may be demonstrated that the angle DGC is also the third part of two right angles : and because the straight F line GC makes with EB the adjacent an- gles EGC , CGB equal ( 13 ...
... third part of two right angles : In the E B same manner it may be demonstrated that the angle DGC is also the third part of two right angles : and because the straight F line GC makes with EB the adjacent an- gles EGC , CGB equal ( 13 ...
Página 106
... third part of the whole contains five ; and the arch AB , which is the fifth part of the whole , contains three ; therefore BC their dif- ference contains two of the same parts : bisect ( 30. 3. ) BC in E ; therefore BE , EC are , each ...
... third part of the whole contains five ; and the arch AB , which is the fifth part of the whole , contains three ; therefore BC their dif- ference contains two of the same parts : bisect ( 30. 3. ) BC in E ; therefore BE , EC are , each ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore